A Thematic Approach to Teaching Liberal Arts

Authors: Lisa Heldke, Professor of Philosophy Email: HELDKE@GUSTAVUS.EDU Phone: (507) 933-7029 Paul Saulnier, Professor of Physics Email: PSAUL@GUSTAVUS.EDU Phone: (507) 933-6123 Gustavus Adolphus College 800 West College Avenue Saint Peter, MN 56082

INTRODUCTION

Undergraduate liberal arts education today is typically conceived along disciplinary lines.

Students major in a particular discipline and often “fill out” their education with “gen ed”

requirements chosen from a cafeteria menu of offerings from other academic divisions. These

divisions often divide students from each other quite literally; treating such differences as those

between the humanities and the physical sciences as unbridgeable chasms. Even in the relatively

small, congenial context of a liberal arts college, such gaps—the science/humanities gap in

particular—can loom large. Students must regularly hopscotch their way across it, as they work

to create a major and fill those gen ed requirements; but they may do so in ways that require

them to engage in relatively little cross-fertilization of ideas. This is because faculty, even at a

liberal arts college, can (to introduce another metaphor) create silos for themselves populated by

members of their own divisions, reducing the chances that they will have to talk or teach outside

their disciplinary comfort zone.

Integrated general education curricula and interdisciplinary majors strive to offer a

different approach to education, but these programs often struggle mightily to avoid falling into

the usual disciplinary way of thinking. A course at our institution, Gustavus Adolphus College,

offers an intentional opportunity for faculty and students to think collectively across disciplinary

boundaries. The course, a senior capstone experience for the college’s alternative integrated

general education program (called the Three Crowns Curriculum, 3CC), is traditionally taught by

a pair of faculty from different disciplines, usually a humanities discipline and a social or natural

science discipline.

This brief paper describes a version of that course created by the authors, a physicist and

a philosopher. We chose to focus the course around a theme—symmetry—that interested both

of us, and that crisscrossed disciplinary and divisional lines. In order to avoid recreating

disciplinary silos within the course, we looked for pedagogical inspiration from John Dewey.

Dewey’s educational philosophy—specifically his philosophy of elementary education—

structured learning not by disciplines, but by themes. This paper will place our co-taught

thematic senior seminar course in context within the curriculum at Gustavus, explore the basis

of the John Dewey inspiration, illustrate an application of Dewey’s pedagogical philosophy by

using symmetry as the basis for a multi-disciplinary course, and finally examine lessons learned

from the experience.

General Education at Gustavus: The Three Crowns Curriculum

Gustavus Adolphus College has long subscribed to the liberal arts tradition of building a

curriculum that incorporates the notion of the one-third/one-third/one-third paradigm.

Specifically, this paradigm espouses the idea that a student’s total course of study should be

roughly divided into three equal parts consisting of general education, major, and elective

courses. At Gustavus, students may complete their general education requirement by

participating in one of two general education programs; the Liberal Arts Perspective (LAP) or

the Three Crowns Curriculum (3CC). While the LAP is closer to a traditional distributive

curricular model, the 3CC pathway is based on a prescribed four-year integrated sequence of

courses. Both of these general education programs are characterized not only by the desire to

expose students to “various ways of knowing” but also to the philosophical underpinnings of

and interchange of ideas among these intellectual perspectives. Indeed, the notion of “ways of

knowing” is so central to the general education program at Gustavus that even in the more

distribution based Liberal Arts Perspective curriculum general education courses are not tied to

particular departments (e.g. courses that satisfy the “Mathematical and Logical Reasoning” or

“The Arts” areas may be offered by a faculty member in the Philosophy Department). A

curriculum built on “ways of knowing” rather than a set of departmentally focused requirements

helps faculty and students fight against the natural insulating properties of the departmental

focused organization so prevalent in higher education today.

As the Gustavus college catalog states, the 3CC curriculum “is a core curriculum in

which integrated courses build upon each other to create a common body of knowledge. A

theme of ‘the individual and community’ is seen throughout the program as it examines the

Western tradition within a global perspective. Students are challenged to address ethical values

questions both in class and the Three Crowns-sponsored cultural, social, and intellectual

activities.” While the Three Crowns curriculum is not an honors program and is thus open to

any entering first-year student, enrollment is limited to approximately 60 students. This student

cohort moves through an integrated set of courses (consisting of multiple sections) that, over

four-years, expose them to the many different ways human understand their place in the

universe. These courses include, Historical Perspectives I & II, Individual and Morality, Biblical

Traditions, Individual and Society, Musical Understanding, Visual Experience, Theatre Arts, The

Literary Experience, Natural World, and the capstone Senior Seminar course. The Senior

Seminar course at Gustavus has traditionally been team-taught by faculty from different

departments (often different divisions) within the College. While the specific topic or content

that a particular seminar chooses to explore is quite open, the Senior Seminar course “calls upon

students to contemplate questions concerning values in the context between the individual and

the community.” It is within this context that we, a philosopher and a physicist, following

American philosopher John Dewey’s lead, offered a Three Crowns senior seminar built upon

symmetry as its central theme.

John Dewey and Thematic Learning

John Dewey wrote on topics ranging from epistemology to aesthetics. However, he is

perhaps most widely known to those outside of philosophy for his work on philosophy of

education, particularly on what was known as “progressive education” in the early-mid twentieth

century. Dewey, and a collection of (mostly women) teachers famously investigated, developed

and operationalized this model of education at the renowned Lab School at the University of

Chicago, a K-12 school still in operation today. When he later moved to Columbia University, he

worked with other education theorists to create the Lincoln School, organized for similar

pedagogical purposes. It should not go unnoticed that this work focused on elementary education.

Be that as it may, the principles and approaches undergirding this model of education proved

useful for us at the college level.

Three aspects of the Deweyan pedagogical model influenced the design of our 3CC

course: a commitment to beginning inquiry from students’ interests and knowledge; an emphasis

on teachers not as “profess-ors” but as facilitators who are themselves learners; and a focus on

topics or themes, as opposed to disciplines.

1. Beginning with students: At the heart of Dewey’s philosophy of elementary

education is his commitment to beginning inquiry at the point of students’ interests and abilities,

and then using that interest and curiosity as a way to prod them to develop and mature in their

thinking. Taking a leaf from this model, the 3CC capstone intentionally prioritized students’

interests, as well as their level of familiarity with technical concepts, for two reasons; first,

because the level of familiarity with technical scientific concepts varied considerably from

student to student (a consequence of their having majors ranging from mathematics to dance);

and second, because the course sought to create a context for inquiry that treated disciplinary

differences among students not as obstacles to be overcome (“she doesn’t know much

literature”; “he hasn’t taken any math beyond finite math”), but as opportunities for more

complex and integrated dialogue. To that end, it was vital that religion students and physics

students felt equally invited to talk, and that all felt welcome to bring their knowledge and

ignorance into the classroom. On this score, the course was advantaged by the fact that the

students in this integrated curriculum had been taking classes with each other for three years by

the time they walked into ours. They knew each other quite well—well enough, in fact, that they

were sometimes unwilling to revisit old disagreements.

2. Teachers as learners and facilitators: In a Deweyan elementary classroom,

ignorance and curiosity went hand in hand; students were encouraged to see their ignorance not

as a shameful problem to be hidden, but as an opportunity for inquiry and investigation. In

young children, fostering a connection between ignorance and curiosity may be simply a matter

of encouraging, rather than stifling, a tendency they have been exhibiting since birth; as students

mature, the challenge becomes greater, because students become more uncomfortable with their

own ignorance.

Teachers thus played a crucial role in fostering student curiosity at all grade levels. In the

progressive classroom teachers operated as learning coordinators, as facilitators who were

themselves curious learners. Their most appropriate title might be “chief learner,” since one of

the most important things they were doing was modeling what it looks like to learn. Such a view

of the educator stood in sharp contrast to traditional models of the day, which held that teachers

were authoritative “content providers.” In a Deweyan setting, teachers did not own the content,

and likely would not even know everything that students would need to learn. Far from being a

problem, however, teachers’ ignorance was an opportunity for students to experience what

genuine (not “pretend”) learning looked like.

In an elementary school classroom, the things a teacher is learning will often be quite

different from the things her students are learning. The latter might be struggling to learn to use

a ruler to measure and cut boards for their boat, while she is learning about boat design in order

to be able to guide their construction. However, in an interdisciplinary college classroom in

which faculty members from different disciplines are teaching together, chances are good that

some students and some faculty might be ignorant in the very same ways about the very same

topics. For a faculty member, displaying such ignorance can be an unnerving experience. If one

believes one’s legitimacy in the classroom stems chiefly from one’s knowledge, not having some

requisite body of knowledge, and confessing one’s ignorance (on a daily or weekly basis!), can

seem suicidal—or at least very disempowering. Such a feeling might be particularly acute in a

team teaching situation with faculty members from very different disciplinary backgrounds.

“Nonscientists” might feel deeply intimidated by having to confess their ignorance of current

scientific thinking; “nonhumanists” might feel embarrassed to admit that they have not read a

particular text that is considered to be a “touchstone” of classical western education.

On a Deweyan model, however, such situations in the college classroom are perhaps the

most valuable teaching situations of all, for they afford students the opportunity to see high-level

learning happening, and to see themselves in their teachers. Fostering cross disciplinary

expressions of ignorance and curiosity might be the most important things a faculty member

might do for their liberal arts students—and, to move beyond the walls of the classroom, one of

the most important things they might do to cultivate in their students the capacity to participate

in public discussion and debate about, e.g., science-based issues, and to do so in ways that resist

the “silo-ing” of knowledge.

3. Themes, not disciplines: Elementary school curriculum, at the time Dewey created

the Lab School, was organized by subjects. Students’ days consisted of blocks of instruction in

particular, discrete subjects: each day, they went from reading to math, to penmanship. Any

connections among these subject matters were happy coincidences, not coordinated efforts. In

contrast, at the Lab School, students’ learning was organized in weeks-long thematic units. All

the elements of a day’s instruction coordinated with each other around the current theme.

Students learned requisite skills in arithmetic, spelling, social studies and science in an integrated

way that focused their attention on concepts and content related to that thematic unit.

For instance, in a legendary unit on boats that was created for third graders at the

Lincoln School, students built and sailed boats, visited the nearby Hudson River, and learned

about the cultures of that river. In the process, they acquired skills and knowledge of history,

geography, arithmetic, literature, writing, and art. (The students and their teacher, Nell Curtis,

actually wrote a book about boats and boat making. (Third Grade Children)) Skills like arithmetic

and spelling were not treated as separate subjects, but were understood organically, in context,

and in relation to each other.

Frankly, this kind of non-disciplinary study might be easier for elementary school

children than for college students. College students (and their teachers) are well aware of

disciplinary divides. They can be persnickety about patrolling the borders of a discipline, and can

also be nervous about venturing outside of the comfort zone of their own discipline. When one

attempts to suspend disciplinary divisions altogether, in order to explore ideas “in general,” it can

make everyone in the room rather nervous.

The inspiration of Dewey did not quell our fears as we taught this course, but it did give

us a sense that what we were doing had legitimacy, and gave us a way to think and teach that felt

credible to us. The next section of the paper explores the particular theme we chose for the

course.

SYMMETRY

We chose symmetry as a theme for this course for a couple very simple reasons. First, it

fascinated each of us independently. Second, it allowed for a tremendous range of flexibility and

breadth; every field of human inquiry or creativity, from music to astrophysics, probably utilizes

symmetry concepts in some way. These two reasons made it an ideal theme around which to

structure the course.

We began the course by introducing students to a technical, scientific notion of

symmetry. With this concept as a kind of touchstone or foundation for further inquiry, we spent

the remainder of the semester exploring a vast array of topics using symmetry as our tool for

investigation. We studied questions in physics (what role does symmetry play in the makeup of

the physical universe?), in aesthetics (what roles does symmetry play in our experience of the

beautiful?), in sex/gender theory (how do intersex and transgender, e.g., challenge notions of

gender binarism and symmetry?), and in ethics (how does thinking of good and evil as a binary

symmetry contribute to ethical reflection?).

Symmetry and the Generalization of the Notion of Symmetry

Many people have a colloquial notion of symmetry that is based upon their lived

experience with two- and three-dimensional objects. For example, one might say a circle

possesses rotational symmetry about an axis passing through its center. What is meant by this is

that if you rotate a circle by any angle about the axis that is perpendicular to the plane of the

circle and passes through its center the figure of the circle remains visually unchanged. It is this

invariance of the circle upon rotation that leads us to say that “the circle possesses rotational

symmetry.” The same may be said of the three dimensional cylinder rotated about its central axis.

In contrast, if one considers the rotation of a square about an axis passing through its center, it is

easy to see that only rotations by 90, 180, 270, or 360 degrees, etc. will leave the appearance of

the square unchanged. An observer who closed their eyes during the rotation of the square

would be unable to detect any change to the square upon opening their eyes only if the square

was rotated about the central axis by the indicated amounts (i.e. 90, 180, 270, or 360). These

everyday examples contain the essential components of geometric symmetry. Namely, in each of

these examples a geometric object (circle, cylinder, or square), had a specific operation

performed on it (a rotation about a specified axis), and an observer noted whether or not the

objected had undergone a detectable change (enabling the observer to determine if the given

object is symmetric with respect to the specified rotation). While geometric symmetry may be

familiar to many (whether or not they can define it formally), the generalization of the concept is

perhaps less well known and certainly less discussed. It provides a powerful lens with which to

view our world. Another way to emphasis the power of symmetry as a concept is to say that

poets and physicists alike can understand themselves to be “up to some of the same things,”

when they realize that symmetry questions shape the endeavors of both.

The essential features contained in the geometric examples of symmetry cited above are

(1) an object is specified, (2) the operation or transformation to be performed on that object

noted, and (3) the invariance of the object under the specified operation is tested. This notion of

symmetry may be ground and polished into a powerful lens by extending (1) to include any idea,

concept, or equation rather than just geometric objects; and by broadening (2) to include

cultural, religious, gender, temporal, mathematical transformations, etc. rather than just simple

rotations. For example, one may study ethics by asking whether or not a particular notion of

“fairness” would be invariant (symmetric) with respect to a shift in time or culture (the

transformation). Additionally, one may explore mathematics by exploring the symmetry

properties of music. Thus, one may study various traditional subjects in an integrated and

interdisciplinary way by using symmetry as a unifying theme.

Symmetry Topics

Symmetry was in many ways an ideal theme for the course, for it so clearly arose as an

important issue in multiple contexts, multiple disciplines. As such, it also served as an ideal

theme with which to engage students; it offered endless points of entry, as well as endless

opportunities to be specialized (if that was their preference) or to be broad and sweeping. This

thematic versatility was displayed in the breath of topics that students chose for their final

reflection papers (discussed below). A specific example, taken from physics, may help to

illustrate the expanded definition of symmetry.

Symmetry holds a central place in physics that goes to very core of the discipline. While

some symmetries in nature are easy to observe as they provide a visible display of underlying

order (e.g. the cubic crystal structure of ordinary table salt is a macroscopic manifestation of

more distant microscopic symmetry), others may be more abstract and require broadening our

notion of symmetry beyond the geometric. The concept of time-reversal invariance is one such

symmetry. Using our expanded definition of symmetry discussed above leads us to identify “the

equations of physics” as our “object” to be transformed and reversing “the arrow time” as our

transformation.

As a specific example, let us consider what happens to the equations of classical

mechanics, as embodied in Newton’s laws of motion, when we reverse the arrow of time (let

time run backwards). Mathematically this is accomplished by replacing every time-variable

in Newton’s second law of motion with its time-reversed counter-part and asking if the

equation remains unchanged (is symmetric) with respect to this transformation. It turns out, that

in the absence of friction; the time-variable only appears in squared form (i.e. ) and thus

when we replace with the equation remains unchanged (since leaving

the equation unchanged). Hence in the absence of friction, the direction of time makes no

difference in the equation of motion and both forward and backward in time motion is allowed

(Newton’s laws of motion without friction are said to be symmetric with respect to a change in

the direction of time). This effect is physically observable when we consider your local applied

physics laboratory (the local pool hall). In the motion of billiard balls on a pool table the drag

caused by friction may be neglected over small distances and therefore this is an excellent model

system to test this symmetry. Consider the collision of two-billiard balls filmed from above. If

someone projected the film for you, would you be able to tell whether or not the film was

running forward or backward? The fact you would be unable to tell which direction represented

the actual experiment performed is a real life manifestation of this time-reversal symmetry. (As a

counter-example, consider being shown a forward and reverse film-sequence of an ice cube

melting. Could you tell which represented the actual experiment performed?)

Symmetry proved to be an enormously fruitful topic to explore. Giving ourselves the

freedom to “play” in the classroom, we spent days watching physics demos, listening to music,

reading poetry, looking at art, watching mathematics videos, and just generally “playing” with the

concepts of symmetry. Using the general concept of symmetry as an anchoring point, we would

frequently come back to ask ourselves—in the midst of reading a poem or looking at a piece of

art—“what’s the transformation here?”, a phrase that reminded us that we were indeed dealing

with “the same” kinds of things, and that also gave us considerable practice in moving flexibly

among deeply disparate topics.

LESSONS LEARNED

Students as Teachers

For us, evidence of the success of our thematic approach to the 3CC capstone lies in the

research projects students prepared for the class. Students (for the most part) chose topics that

emerged from their disciplinary perspectives, and then presented the results of their research in

both oral and written form at the end of the class. One mathematics student’s research question

was, “which do we find more aesthetically pleasing, a tree branch with high symmetry, or a

branch with broken symmetry?” She wrote a computer program to create fractal images, and

then conducted some qualitative research to find out how others responded to the images. A

dance student led the entire class in simple movements, designed to give us an understanding of

how our bodies create, disrupt, and reestablish symmetry in dance. A biologist looked at the

moment in embryonic development when the embryo exhibits its first asymmetry. A chemist

decided to break out of his major, to explore the relationships between Old and New

Testaments as symmetry relations. Discussions of each project were freewheeling, multi- and

inter-disciplinary—though admittedly the most technically scientific talks still tended to get the

most timid responses from nonscientists.

Team Teaching

Lisa reflects: Paul and I are both regarded as excellent teachers. So why were we both so

terrified about teaching “in front of each other” in this class? This question fascinated and

frustrated both of us for the duration of the semester. Only toward the very end of the semester

did each of us finally find ourselves comfortable being our “pedagogical selves” in the classroom.

For me, the nervousness sprang largely from a kind of internalized dismissal of the legitimacy of

philosophy, when compared to the “hard science” of physics. I found myself imagining and

anticipating criticisms from Paul before he even had a chance to read the material I had assigned.

I simply assumed that he would think philosophy was “stupid,” that its questions were “the

wrong ones,” or that “physics could deal with them better.” Of course my nervousness wasn’t

entirely fantastical; we are living in an era in which prominent physical scientists regularly declare

philosophy “dead.” But Paul is not among those scientists—and this was not a philosophy class,

even though I brought my philosophical self into the room with me each day.

I believe that the profundity of this challenge also represented one of the most important

pedagogical opportunities of the class—for us and for the students. As noted above, the model

of inquiry advocated by Dewey emphasizes the teacher as facilitator and learner. Arguably, this

role is nowhere more important than in a college classroom where students can witness well-

educated professors from different disciplines express their ignorance to one another, and learn

from each other.

One memorable conversation, for instance, explored the question “what role, if any,

does ‘truth’ play in scientific inquiry. The conversation took both instructors down to the barest

bones of our respective disciplines, and left us understanding a little bit more about the way that

we and our students live the gap between the humanities and the physical sciences. (It left me

pondering the question “whose disciplinary standards are in play when everyone is trying to have

a conversation outside of their home discipline? What, if any, are the underlying assumptions

upon which we can build our discussion?”) It is not an exaggeration to suggest that such

conversations can model for students what it means to be an active and informed member of a

democratic society. For Dewey, democracy is education; learning to be actively ignorant is thus a

vital skill for any member of a democratic society.

Paul reflects: As a faulty member who is perhaps most comfortable at a blackboard filled

with equations or down in a dark basement optics research laboratory, this seminar course both

challenged and provided an opportunity for growth. For me, the challenge lay both in the varied

course content as well as its format. The breath of content explored in the course was expansive

not only because the instructors came from disparate backgrounds, but also since students were

encouraged, and indeed required, to explore the notion of symmetry in their respective

disciplinary homes and encouraged to make connections with those of other seminar

participants. One day might find the group discussing symmetry in literature or poetry, while

another might find us in a dance studio exploring the symmetry inherent in our own biological

form and movements, and yet tomorrow may bring a student led discussion of bio-chemistry or

religion. The benefits of Dewey’s notion of shared multifaceted learning are clearly on display in

this type of theme-based seminar course.

As a physicist, the other lasting impression that I take away from this course is an

appreciation for just how freeing the experience was. In my discipline there are certain canonical

sub-fields that must be taught to prepare students for graduate school and within each of these

there are a set of topics that must be addressed. While each instructor has some freedom as to

how to best facilitate learning, at the end of the semester students are expected to have attained a

certain level of understanding as the sequential nature of the discipline makes it likely that

student proficiency will be probed in the next course by the subsequent professor. The

wonderful amorphous nature of symmetry as a theme allowed us to introduce personal passions

into the seminar (e.g. poetry and guitar). Rather than being seen as “self-indulgent”, students

appreciated the personal nature of this “sharing” and, at least some, inherently understood that it

represented a model of life-long liberal learning.

CONCLUSION

John Dewey is often invoked as an inspiration for contemporary conceptions of the

liberal arts, and their connection to the institution of democracy. We find inspiration for

contemporary liberal arts education in a different aspect of Dewey's thought, however-- namely,

his philosophy of elementary education. We have explored the way in which conceptual or

thematic focused courses may be used in the liberal arts college setting to great effect. The team-

taught seminar course explored the unifying concept of symmetry from multiple vantage points

and disciplinary and interdisciplinary perspectives. With symmetry, in all its conceptions, as the

organizing principle our course explored such diverse topics as space-time, the nature of reality,

matter and antimatter, sex and life, beauty, morality, and meaning and being. We found this

theme-based approach to multidisciplinary teaching to be challenging, engaging and freeing for

both students and us, in ways that embody the spirit of the liberal arts. We believe that it may

serve as a model for others as liberal arts colleges move into the 21st century.

Works Consulted

Dewey, John. Democracy and Education. Vol. 9 of The Middle Works of John Dewey. Ed. JoAnn

Boydston. Carbondale: Southern Illinois University, 2008. Print.

-----. Experience and Education. New York: The Free Press, 1997. Print.

Third Grade Children and their Teacher, Nell C. Curtis. Boats: Adventures in Boat Making. Chicago:

Rand McNally, 1927.

http://babel.hathitrust.org/cgi/pt?id=uc1.$b262013;view=1up;seq=7.

Darvas, György. Symmetry. Berlin: Birkhäuser Verlag, 2007. Print.

Goldberg, Dave. The Universe in the Rearview Mirror. New York: Dutton/Penguin, 2013. Print.